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Search: id:A035348
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| A035348 |
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Triangle of a(n,k) = number of k-member minimal covers of an n-set (n >= 1, k >= 1). |
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+0
10
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| 1, 1, 1, 1, 6, 1, 1, 25, 22, 1, 1, 90, 305, 65, 1, 1, 301, 3410, 2540, 171, 1, 1, 966, 33621, 77350, 17066, 420, 1, 1, 3025, 305382, 2022951, 1298346, 100814, 988, 1, 1, 9330, 2619625, 47708115, 83384427, 18151560, 549102, 2259, 1
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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These are what Clarke calls "Minimal disordered k-covers of labeled n-set".
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REFERENCES
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R. J. Clarke, Covering a set by subsets, Discrete Math., 81 (1990), 147-152.
Hearne and Wagner, Minimal covers of finite sets, Discr. Math. 5 (1973), 247-251.
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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E.g.f.: Sum((exp(y)-1)^n*exp(y*(2^n-n-1))*x^n/n!, n=0..infinity). - Vladeta Jovovic (vladeta(AT)eunet.rs), May 08 2004
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EXAMPLE
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1; 1,1; 1,6,1; 1,25,22,1; ...
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PROGRAM
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(PARI) C(n, k) = if(k<0|k>n, 0, n!/k!/(n-k)!); a(n, k)=sum(i=0, k, (-1)^i*C(k, i)*(2^k-1-i)^n)/k!; printp(matrix(10, 10, n, k, a(n-1, k-1)))
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CROSSREFS
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Row sums are A046165. Cf. A049055, A003465, A002177.
Sequence in context: A060187 A156139 A155863 this_sequence A140945 A141688 A166960
Adjacent sequences: A035345 A035346 A035347 this_sequence A035349 A035350 A035351
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KEYWORD
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nonn,tabl,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Entry improved by Michael Somos
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